The non-destructive investigation of samples is an important object in various technical fields like material sciences, medical examinations, archaeology, construction technique, techniques concerning security matters etc. One approach for obtaining an image of a sample e.g. by computer tomography (CT) is based on an irradiation trough a sample plane from different projection directions with X-rays, followed by the reconstruction of the sample plane on the basis of attenuation data measured at different directions. The entirety of the measured attenuation data can be described in terms of so-called Radon data in a Radon space.
Different reconstruction methods for Radon data are known today, which in particular comprise iterative reconstruction methods and filtered back-projection methods. A further improved method of reconstructing image functions from Radon data is described in EP 04031043.5. With this method of using orthogonal polynomial expansions on the disk (in the following: OPED algorithm), an image function representing the region of investigation is determined from Radon data as a sum of polynomials multiplied with values of projection functions measured corresponding to a plurality of predetermined projection directions through the region of investigation.
The image function obtained with the OPED reconstruction methods is a continuous function. As typical devices for image visualization have a digitized output, the continuous function is subjected to a discretization for presenting a visualized image. As an example, displaying the image function on a computer display or printing the image function with a digital data printer requires a discretization of the image function according to the screen resolution of the display or printer. As an example, the continuous image function is discretized with a pattern of 512*512 or 1024*1024 pixels. One value of the image function converted into a gray value is assigned to each of the pixels, respectively.
The conventional imaging techniques have a common disadvantage, which is associated with the discretization of the continuous image function. Usually, the local resolution of the visualized image is essentially smaller compared to a space frequency of local image function features. The pixel size of the visualized image is essentially larger compared to the size of local image function features. As the conventional discretization comprises a convolution of the image function with a Dirac function (delta function, unit impulse function) at each pixel, local features of the continuous image function can introduce distortions into the visualized image. As a result, artifacts can occur in the image in particular if local features of the image function have a characteristic period of high-frequency components of the image function being comparable with the pattern of discretization.
The above disadvantage is associated not only with the conventional CT imaging, but also with all available OPED reconstruction and image processing methods based on the collection of Radon data, like e. g. neutron transmission imaging, ultrasound tomography etc.